0
votes
1answer
8 views

Find the Laplace transform of integral(from 0 to x) sin(2t) dt

Find the Laplace transform of integral(from 0 to x) sin(2t) dt So basically, integral(from 0 to x) sin(2t) dt = -0.5[cos2x - 1] So L[cos2x] = s/(s^2 + 4) L[-1] = L[-delta(x)] = -1 So I got the ...
0
votes
1answer
14 views

Laplace transform, Inverse Laplace transform

Let $(\mathcal{L}f)(s)$ be the Laplace transform of a piecewise continuous function $f(t)$ defined for $t\geq 0$. If $(\mathcal{L}f)(s)\geq 0$ for all $s\in\mathbb{R^+}$ does this imply that $f(t)\geq ...
1
vote
0answers
51 views

Z - transform of a transfer function

I have to apply a z-transformation to my transfer function which looks like this: $$\frac{K}{s} - \frac{K\cdot T}{T\cdot s}+1$$ I have tried it and this is my result: $$K \cdot \frac{z}{z-1} - K ...
0
votes
1answer
65 views

Z-transform a transfer function

Could someone help me invers Z-transform of this transfer function. $H_k(z) = \frac{Y_k(z)}{X(z)} = \frac{1}{1-cos(\frac{2·\pi ·k}{N})·z^{-1}+z{^-2}}$
1
vote
0answers
67 views

Calculating convolutions of probability density functions

I have a PDE: $$\frac{\partial N (x,u)}{\partial x}=\int _0^uN(x,u)f(u-u')du'$$ $$N(0,u) = \delta (u)$$ Here $f(u)$ is a probability density function for $0 \le u \le u_{max}$, $\int _0 ^ {u_{max}} ...
0
votes
0answers
34 views

reference text for all transforms

I want to learn Fourier and laplace transform by myself.I have learnt 'calculus-one variable' and beginning to enter 'calculus-multiple variables'.can anybody tell any good books for begin studying ...
0
votes
1answer
74 views

If $f$ has a Laplace transform $F$ then $\lim_{s\to\infty}F(s)=0$?

As I know, well-known functions that have Laplace transform vanishes at infinity. Because almost well-known functions has exponential form and the Laplace transform of function has exponential form ...
1
vote
1answer
58 views

Take Laplace Transform of the integral J_0

I was just wondering how to use tables from Spiegal to solve $\int_0^\infty J_0(2\sqrt{ut}) J_0(u) du$ At the moment, I see similar transforms on page 244, but I don't actually know how to combine the ...
1
vote
0answers
62 views

Transformed Laplace “solution space”

From my own knowledge I can tell that when we take the Laplace transformation of a function we are in essence transforming our f(t) into a F(s). I've looked at several Q/A here asking for the ...
0
votes
1answer
41 views

inverse transform of $Z(\omega) =\frac{a}{\alpha-i\omega}$

I am stuck at calculating the inverse transorm of $Z(\omega) =\frac{a}{\alpha-i\omega}$. Can someone help me please? thanks
1
vote
2answers
115 views

Laplace Transformation Applications

In one of our Mathematics lecture our Prof told us that similar to Logarithmic Transformations we can use Laplace Transformations to solve difficult equations. What kind of equations do Laplace ...
4
votes
2answers
130 views

Fourier, Laplace, … and other Integral-transformations

I know Laplace, Fourier and Mellin-Transformation. Is there a general theory of transformations? My main interest is about classification of transformations satisfying specified properties like ...
1
vote
2answers
64 views

How do a transformation 'born'?

Well, there are several transformations in math. Like the laplace transformation. My question is about the utility and motivation of these transformations. Like, when we have an equation, and we ...
0
votes
2answers
137 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
5
votes
1answer
1k views

How to figure of the Laplace transform for $\log x$?

I was looking at a table of common Laplace transforms of functions when I came across the transform for $\log x$. Apparently, the transform is as follows: $$\mathcal{L} \left\{ \log ...
2
votes
2answers
244 views

Does this Laplace transform exist?

I had a final in differential equations with the first question being: "1. Does the Laplace transform of $\displaystyle \frac{1}{(1+t)}$ exist? Why or why not?" and number 2 was "2. If number one ...